Razzle-dazzle, Indian-style—that's Mumbai, the former Bombay, the country's seaside financial capital and trendsetting East-West nexus. India's greatest port and the capital of Maharashtra state, Mumbai perches on the Arabian Sea, covering an island separated from the rest of India by a winding creek. A world unto itself, Mumbai hits you with an intensity all its own. It is distinctly tropical, with pockets of palm trees and warm, salty breezes—and its culture is contemporary, vibrant, and often aggressive, reflecting both the affluence and poverty of the nearly 20 million people crowded onto this island. Behind all this, weathered Victorian mansions, some still privately owned, and grand public buildings, many beautifully lit at night, stand as lingering reminders of the British Raj.

In 1995 Bombay's name was officially changed to Mumbai, after Mumba Devi, the patron Hindu goddess of the island's original residents, the Koli fishermen. However, many residents still call their city Bombay. It's confusing, but just another chapter in the city's labyrinthine history.

Mumbai initially consisted of seven marshy islands—Colaba, Old Woman's Island, Bombay, Mazgaon, Worli, Mahim, and Parel—belonging to the Muslim kings of the Gujarat sultanate. The Muslims passed the parcel to the Portuguese (who occupied much of western India in the 16th and 17th centuries), who in turn passed it in 1661 to England's King Charles II as part of a dowry in his marriage to the Portuguese Princess Catherine de Braganza. The British established a fort and trading post that grew quickly in size and strength.

Soon enough, land reclamation joined the seven small islands into one, grafting a prototype for today's multifarious metropolis. The pride of the British in Bombay, and in their power over western India, is memorialized in the city's most celebrated landmark—the Gateway of India, built to welcome King George V to India in 1911. Ironically, it's now near a statue of the young 17th-century Marathi leader, Shivaji.

The Mumbai you see today is a city of mind-boggling contrasts: sometimes exciting, sometimes deeply disturbing. As your plane descends toward the runway, usually late at night, your first view of Mumbai takes in vast stretches of slums, stacked and piled onto each other like cardboard boxes—only a fleeting glimpse of the staggering poverty that coexists, invariably side by side, with the dazzling wealth flashed in trendy boutiques and deluxe hotels. In the neighborhoods of Churchgate or Nariman Point, Mumbai's slick hotel and business centers, a fleet of dark-suited executives may breeze by on its way to a meeting while a near-naked little girl with matted hair scavenges in the gutter beside them. A fancy department store is across the road from a group of shacks that a few hundred people call home—one customer in that store may spend more in an hour than all the people living in the shacks earn in a month. A journalist once pointed out that Mumbai is a city where the servant walking the pedigreed, handsomely groomed dog has no formal education, but his charge has been to an expensive training school.

It's important to view Mumbai in perspective. Mumbai can seem so different from the rest of India that it could be another country. It operates according to its own rules, and its pulse beats far more quickly than the rest of the country, which views it as the city of opportunity. Mumbai tantalizes millions with prospects of wealth and success. Every day, migrants arrive—be they business-school grads or laborers—to see if they too can make a life here. Apart from the city's original Maharasthrian population, every Bombayite, from the hijra (eunuch) to the taxi driver to the white-collar worker, is, as hard as it may be to believe, living out his or her dream—in a hovel or a palace. More often than not, Bombay is a place to build a better life.

For the traveller, Mumbai is both disturbingly eye-opening and incredibly exciting. Here in the heady sun and breeze of the Arabian Sea you can feast in fabulous restaurants, bargain in street bazaars, browse in exclusive boutiques, take a horse-drawn ride past stately old Victorian buildings, get lost in the stone carvings of the 7th-century Elephanta Caves, watch the sun rise over the Gateway of India, and stroll at sunset along Marine Drive's endless waterfront promenade.